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A136412 a(n) = (5*4^n+1)/3. 7
2, 7, 27, 107, 427, 1707, 6827, 27307, 109227, 436907, 1747627, 6990507, 27962027, 111848107, 447392427, 1789569707, 7158278827, 28633115307, 114532461227, 458129844907, 1832519379627, 7330077518507, 29320310074027 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

An Engel expansion of 4/5 to the base b := 4/3 as defined in A181565, with the associated series expansion 4/5 = b/2 + b^2/(2*7) + b^3/(2*7*27) + b^4/(2*7*27*107) + .... Cf. A199115 and A140660. - Peter Bala, Oct 29 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-4).

FORMULA

a(n) = 4*a(n-1)-1.

O.g.f.: -(-2+3*x)/((-1+x)*(-1+4*x)). - R. J. Mathar, Apr 04 2008

a(n) = 5*a(n-1)-4*a(n-2). - Vincenzo Librandi, Nov 04 2011

PROG

(MAGMA) [(5*4^n+1)/3: n in [0..30]]; // Vincenzo Librandi, Nob 04 2011

(Haskell)

a136412 = (`div` 3) . (+ 1) . (* 5) . (4 ^)

-- Reinhard Zumkeller, Jun 17 2012

(PARI) a(n)=(5*4^n+1)/3 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A007583. Cf. A007302. A140660, A181565, 1/3 of A199115.

Sequence in context: A150592 A150593 A024429 * A192417 A150594 A150595

Adjacent sequences:  A136409 A136410 A136411 * A136413 A136414 A136415

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Mar 31 2008

EXTENSIONS

Formula in definition and more terms from R. J. Mathar, Apr 04 2008

STATUS

approved

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Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)